Pentagon chief Ashton Carter said during his first visit to Baghdad Thursday that the United States was willing to do more to help Iraq defeat the Islamic State group.
But the defence secretary said the offer was conditional on Iraqi forces shaping up after the debacles that has seen them lose large cities such as Mosul, Tikrit and Ramadi.
"We are willing to do more... when and if (the Iraqis) develop capable, motivated forces of their own that can take and retain territory," he said as he met some of the 3,500 US military trainers and advisers in Iraq.
His visit came as Iraqi troops, some of which were trained by the United States, tightened the noose on IS in Ramadi, the capital of Anbar province which the government lost in May.
On his first visit since taking office earlier this year, Carter met Prime Minister Haider al-Abadi and his counterpart, Khaled al-Obeidi.
He also met a number of top Sunni politicians, including officials from the regions most affected by the massive onslaught the extremist Sunni IS launched in June 2014.
Government and allied forces recaptured Tikrit in April but any attempt to take back Mosul, the capital of Nineveh and the largest city in the "caliphate" IS proclaimed over parts of Iraq and Syria last year, has been put on the back burner.
The government has instead focused on Anbar, the vast western province that stretches from the Syrian, Saudi and Jordan borders all the way to the outskirts of Baghdad.
- Trainees join battle -
US-led coalition aircraft, which have carried out thousands of strikes in Iraq and Syria during the past year, have lately been hitting dozens of targets in Anbar every week.
"Iraqi security forces are in the process of encircling" Ramadi, said Pentagon spokesman Colonel Steve Warren, who is travelling with Carter.
He put the number of jihadist fighters defending the city at 1,000 to 2,000.
He would not say when he thought a drive to wrest the city from IS might be launched in earnest but said it should be a matter of "weeks".
Since their deployment, US military advisers have trained 9,000 soldiers, but they had not seen frontline action until a first batch of 3,000 recently joined the Ramadi battle, Warren said.
"This is a development we are very satisfied to hear," he said in Baghdad.
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Several hundred US troops are also helping Iraqi forces train local Sunni Arab tribesmen at a large base in Habbaniyah, between Ramadi and the jihadists' other Anbar bastion of Fallujah.
Warren said 1,800 tribal fighters had already received training and equipment.
- Tribes want more -
But Anbar tribal leaders want more from Washington.
"The coalition's support to Anbar and its sheikhs is weak on all levels, mainly the humanitarian level... and the security level when it come to support for the tribes in liberating their areas," Rafia al-Fahdawi, a tribal leader whose forces have been fighting alongside the government.
US officials criticised the performance of the army in the aftermath of the fall of Ramadi.
Carter's comment Thursday signalled a reluctance to further ramp up support if Iraq's leaders failed to reform what has been described as a "checkpoint army" into a leaner and more effective professional force.
Washington is also concerned the army will end up playing second fiddle to the Hashed al-Shaabi, an umbrella for Iranian-backed Shiite militias whose fighters have shown determination and often played a lead role in the fightback.
Tehran is Baghdad's other main partner in the fight against IS but is not part of the coalition.
While this month's historic nuclear deal opened a new chapter in relations between Tehran and Washington, their coexistence on Iraq's battlefield remains uneasy.
The army, backed by Washington, wants to take back Ramadi first, but the Hashed al-Shaabi has made Fallujah, the other main city in Anbar, its priority.
After initially expanding in the wake of its proclamation of a "caliphate" over parts of Iraq and Syria last summer, the group led by Abu Bakr al-Baghdadi has seen the internationally supported Iraqi fightback roll back its borders.
The jihadists are also under pressure in Syria, where they have lost several key areas along the border with Turkey.
Observers have warned that as military pressure on IS mounts, the group could revert to its old tactics of hit-and-run attacks and car bombs.
It claimed one of the biggest suicide car bomb attacks in Iraq's bloody history last week and a string of deadly blasts in the capital on Tuesday and Wednesday.